I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this).
Recall: In a ...

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator):
$$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...

I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this.
For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...

I am not able to understand the definition of the density operator. I know that if $V$ is a vector space and if I have $k$ states belonging to this vector space, say $|\psi_{i}\rangle$ for $1\le i\le ...

In my class it was told that ensemble decompositions of a density operator $\rho$ are not unique, but that the ones that exist are related by a unitary operator. I'm trying to prove this, but I get ...

What can we say about the quantum state from the number of zero and non-zero eigenvalues of the corresponding density matrix? Anything related to entanglement or any other properties? Does they vary ...

I'm reading something about quantum information/quantum computing theory, and I've run into a wall. I know what is meant by an equivalence class and how something can be partitioned into equivalence ...

In this paper, on the page 5
http://math.ucsd.edu/~dmeyer/research/publications/qstrat/qstrat.pdf
in the second paragraph:
his first action puts the penny into a simultaneous eigenvalue 1 eigenstate ...

I have looked in Stack Exchange about density matrices but haven't found any answers. What are density matrices and how do they work? What are they used for?
(Also, please tell me what is wrong with ...

In the microcanonical ensemble $(E,V,N)$, the density operator is
$$\hat{\rho}=\frac{\delta(\hat{H}-E\,\hat{I})}{Tr(\delta(\hat{H}-E\,\hat{I}))}$$
Where $\hat{H}$ is the Hamiltonian of the system and ...

The density of states in quantum mechanics is obtained via the rather not so complicated relation below: $$\rho(E)=\delta (E-E_n)$$
Which means that if we know the energy quantization condition for a ...

We consider a system of two particles of spin $\frac{1}{2}$, each described by the two-dimensional one-particle Hilbert space $\mathcal{H}$. Let $|\pm\rangle\in\mathcal{H}$ denote the eigenvectors of ...

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix.
If there's any information ...

I'm having a little trouble understanding what positive-operator valued measure (POVM) are- in particular why/how they are non-negative. For instance, if they just represent measurements, what about ...

Is it possible to construct a well defined inner-product (and therefore orthonormality) within the set of self-adjoint trace-class linear operators? In the affirmative case, dynamics could be analyzed ...

I am studying the time evolution of a density matrix using the Lindblad equation.
My initial density matrix is $\rho(0)=|\alpha\rangle\langle\alpha|$, where $|\alpha\rangle$ is a coherent state. Then ...

Let us consider a initial total quantum system as $\rho(0) = \rho_S(0)\otimes\rho_B$ where $\rho_S(0)$ is initial open system and $\rho_B$ is density matrix for environment.
We can use partial trace ...

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument.
Consider a biparte system $AB$, described ...